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Simplifying 5m2 + -5m + -5 = 2 Reorder the terms: -5 + -5m + 5m2 = 2 Solving -5 + -5m + 5m2 = 2 Solving for variable 'm'. Reorder the terms: -5 + -2 + -5m + 5m2 = 2 + -2 Combine like terms: -5 + -2 = -7 -7 + -5m + 5m2 = 2 + -2 Combine like terms: 2 + -2 = 0 -7 + -5m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -1m + m2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -1m + 1.4 + m2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -1m + m2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -1m + m2 = 0 + 1.4 -1m + m2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -1m + m2 = 1.4 The m term is -1m. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1m + 0.25 + m2 = 1.4 + 0.25 Reorder the terms: 0.25 + -1m + m2 = 1.4 + 0.25 Combine like terms: 1.4 + 0.25 = 1.65 0.25 + -1m + m2 = 1.65 Factor a perfect square on the left side: (m + -0.5)(m + -0.5) = 1.65 Calculate the square root of the right side: 1.284523258 Break this problem into two subproblems by setting (m + -0.5) equal to 1.284523258 and -1.284523258.Subproblem 1
m + -0.5 = 1.284523258 Simplifying m + -0.5 = 1.284523258 Reorder the terms: -0.5 + m = 1.284523258 Solving -0.5 + m = 1.284523258 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + m = 1.284523258 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = 1.284523258 + 0.5 m = 1.284523258 + 0.5 Combine like terms: 1.284523258 + 0.5 = 1.784523258 m = 1.784523258 Simplifying m = 1.784523258Subproblem 2
m + -0.5 = -1.284523258 Simplifying m + -0.5 = -1.284523258 Reorder the terms: -0.5 + m = -1.284523258 Solving -0.5 + m = -1.284523258 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + m = -1.284523258 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = -1.284523258 + 0.5 m = -1.284523258 + 0.5 Combine like terms: -1.284523258 + 0.5 = -0.784523258 m = -0.784523258 Simplifying m = -0.784523258Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.784523258, -0.784523258}
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